Plan B math: AoPS Number Theory or Counting and Probability?

[elegantlion]

Right now I have two math classes scheduled for next year, geometry and algebra 2. This is ds' request so he'll be lined up to take calculus his senior year.

 

I'd like to have a back-up plan in case it's too much. I'd like to keep a math credit in place, probably 1/2 credit. Which of these two AoPS books would you choose? Ds is interested in programming, and languages in general. Is there one that would be more relevant to that field?

 

ETA: This wasn't clear, sorry for the confusion. We would do geometry AND one of the AoPS books, so 1.5 credits of math instead of 2.

[regentrude]

I do not fully understand your request- you want this in addition to the two math credits he already does, or instead???

 

We did C&P; very enjoyable and a good intro to probability; a thorough understanding of probability will be helpful for advanced probability theory and statistical physics later on.

I have not seen the number theory book. Number theory is indeed used for cryptography, so may be relevant to a computer science major eventually, but I find that probability has more applications. Number theory is a great playground, cool puzzles- may be great for a student who enjoys this kind of stuff, but applications will not be immediately obvious.

[elegantlion]

I do not fully understand your request- you want this in addition to the two math credits he already does, or instead???

 

We did C&P; very enjoyable and a good intro to probability; a thorough understanding of probability will be helpful for advanced probability theory and statistical physics later on.

I have not seen the number theory book. Number theory is indeed used for cryptography, so may be relevant to a computer science major eventually, but I find that probability has more applications. Number theory is a great playground, cool puzzles- may be great for a student who enjoys this kind of stuff, but applications will not be immediately obvious.

 

Not in addition to the 2 maths. This would be an alternative plan if doing geometry and algebra 2 concurrently is too much for him.

 

We would do geometry and the AoPS book.

[kiana]

Frankly I do not think you can go wrong with either, but my personal choice would be the probability text.

 

Another option you might consider, if 1.5 credits works for your son, is doing geometry and half of algebra 2. Then, next year, you could do the other half of algebra 2 and precalculus. Even if two math classes at once is difficult for him, if he really wants to get to calculus as a senior he should be able to get there by working through the summer.

[elegantlion]

Frankly I do not think you can go wrong with either, but my personal choice would be the probability text.

 

Another option you might consider, if 1.5 credits works for your son, is doing geometry and half of algebra 2. Then, next year, you could do the other half of algebra 2 and precalculus. Even if two math classes at once is difficult for him, if he really wants to get to calculus as a senior he should be able to get there by working through the summer.

 

Thank you, those are good options as well.

 

 

It sounds like the probability book would be more relevant. If he were younger the number theory book sounds like fun.

[Julie of KY]

We found the counting and probabliity book to be more enjoyable. I know others like NT better, however.

[Cosmos]

Frankly I do not think you can go wrong with either, but my personal choice would be the probability text.

 

Another option you might consider, if 1.5 credits works for your son, is doing geometry and half of algebra 2. Then, next year, you could do the other half of algebra 2 and precalculus. Even if two math classes at once is difficult for him, if he really wants to get to calculus as a senior he should be able to get there by working through the summer.

 

That makes a lot of sense. If your goal is to get through the traditional math sequence all the way to calculus, then a detour for either probability or number theory doesn't really make sense. Why not just work as much algebra 2 as he can handle alongside the geometry? Even if he can't finish it in one year, all his math energy is going toward getting him closer to his goal.

[elegantlion]

 

That makes a lot of sense. If your goal is to get through the traditional math sequence all the way to calculus, then a detour for either probability or number theory doesn't really make sense. Why not just work as much algebra 2 as he can handle alongside the geometry? Even if he can't finish it in one year, all his math energy is going toward getting him closer to his goal.

 

True, but if he stalls out with the algebra 2 I want a back-up plan. His learning doesn't progress at a linear rate, he tends to make leaps. He also has a fine line between pushing and becoming overwhelmed and shutting down.

 

We had a case of that this year and I didn't have a back-up. When we're rolling out the new year I have a harder time coming up with alternate plans. We lost a few weeks of progress because of it.

 

So, I'm trying to head off that panic and creating alternate plans, just in case, in a few subjects. I'm pretty sure he'll be fine with geo and algebra 2, but I've thought that before about a lot of things (not just school) and those seem to be the plans that fall apart the soonest. Yeah, it's February.

[Cosmos]

 

True, but if he stalls out with the algebra 2 I want a back-up plan. His learning doesn't progress at a linear rate, he tends to make leaps. He also has a fine line between pushing and becoming overwhelmed and shutting down.

 

In that case, couldn't he just work extra on geometry? Or just take a break the algebra 2 for while until his brain catches up.

 

It just seems like you're trying to fill a gap, when there is no gap. :) Of course, the probability and number theory books are very interesting and fun topics, so if you want to do them, why not?

[elegantlion]

In that case, couldn't he just work extra on geometry? Or just take a break the algebra 2 for while until his brain catches up.

 

It just seems like you're trying to fill a gap, when there is no gap. :) Of course, the probability and number theory books are very interesting and fun topics, so if you want to do them, why not?

 

Well this may all be a non - issue, everything is speculation at this point. I'm actually trying to fill *my* weakness of assuming everything will be okay and not being prepared in case of issue. Hopefully there will be no gap.

 

Part of the issue is that I have two credits of math scheduled. If (and it's all speculation at this point) I have to drop one of those credits that leaves him one less credit for the year. I don't want to leave him with 6 credits instead of 7. My minimum requirement is 6.5 credits, preferably 7, and I'd want him to fill that in with some sort of math credit. I don't really want to do them, but I'm trying to plan for all contingencies.

[Shelly in VA]

No advice, other than to say that ds16 is currently working through the Probability and Counting book, and he is starting the online Number Theory class next week. There wasn't a reason to the order for us, other than that he wanted the P&C for some of the work he's encountering in Mandelbrot this year, and a friend from Mandelbrot was signed up for the Number Theory class, so he decided to take it along with him. I think either would be interesting to your son, b/c the approach in the AoPS books really has them look at math in a different way than most texts, and that "mathematical thinking" is applicable to all of their math efforts.

 

Also, ds has already finished Algebra I and II, and Geometry, but I don't know that any of that specifically matters for the AoPS courses you are considering.